Constraints on Brane-Localized Gravity

TL;DR

This paper investigates the geometric and physical constraints of embedding 3-branes with spatial curvature into 5D spacetimes, revealing limitations on gravity localization due to bulk cosmological constants.

Contribution

It demonstrates that specific relations between bulk and brane matter are required for consistent embeddings and shows that a bulk cosmological constant cannot localize gravity in curved brane scenarios.

Findings

Bulk cosmological constant cannot produce exponential suppression for gravity localization.

Consistency of embeddings imposes specific relations between bulk and brane parameters.

Embedding of curved 3-branes requires particular matter source conditions.

Abstract

In this paper we explore some general aspects of the embeddings associated with brane-localized gravity. In particular we show that the consistency of such embeddings can require (or impose) very specific relations between all the involved bulk and brane matter source parameters. We specifically explore the embeddings of 3-branes with non-zero spatial 3-curvature $k$ into 5-dimensional spacetime bulks, and show that for such embeddings, a 5-dimensional bulk cosmological constant is not able to produce the exponential suppression of the geometry thought necessary to localize gravity to the brane.